The Chumash in Shemot 23:14 begins describing the three regalim: Pesach, Shavuot, Sukkot, in that order. In Pasuk 17, the Chumash begins again with Pesach and Shavuot. Instead of listing sukkot again in that second list, the Pasuk mentions the prohibition of mixing meat and dairy (cooking a kid in its mother's milk.)

What happened to sukkot? What's the connection between meat and dairy and the regalim?

1 Answer
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…and so gave another rule related to Sukos, saying "You shall not boil a kid in its mother's milk".…

It seems to me… that idolators would do this when they got together: that is, they'd boil kids in milk when they harvested grain, thinking that they would thereby appeal to their god and get close to him, and he would instill blessing in what they were doing…. And certainly that the shepherds would do so when they gathered to do their thing: their food then was kids boiled in milk and all sorts of cooked meat-and-milk dishes. Even nowadays in Spain all the shepherds gather twice a year for a council meeting… and their food is meat and milk — and kid meat is the one they like best in that dish. I also looked into the matter and ascertained that in the far island called England, which has many sheep, more than around these parts, they always do this too.

I think that really it was for this reason that God warned them that when they gather at Sukos they must not cook a kid in milk as [non-Jews] do. And to distance them utterly from the way of idolatry, He forbade eating it, deriving benefit from it, and cooking it….

I do not understand how the meat-and-milk command relates to Sukos, but he clearly states that it does, which is an answer to your question. It may be simply the fact that the idolators would cook meat in milk when they harvested grain (as he writes), which is at Sukos.

(A note on the translation: I use "kid", "sheep", and "shepherd", but all three original Hebrew words really refer to both sheep and goats: "young animal", "sheep/goat", and "shepherd/goatherd" would be more accurate but less wieldy translations.)